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At least 847 records · Page 47
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

2D Dilaton Gravity and the Weil–Petersson Volumes with Conical Defects

We derive the Weil-Petersson measure on the moduli space of hyperbolic surfaces with defects of arbitrary opening angles and use this to compute its volume. We conjecture a matrix integral computing the corresponding volumes and confirm agreement in simple cases. Here, we combine this mathematical result with the equivariant localization approach to Jackiw-Teitelboim gravity to justify a proposed exact solution of pure 2d dilaton gravity for a large class of dilaton potentials.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

The forward physics facility: Physics opportunities and conceptual design

The Forward Physics Facility (FPF) is a proposed extension of the HL-LHC program designed to exploit the unique scientific opportunities offered by the intense flux of high energy neutrinos, and possibly new particles, in the far-forward direction. Located in a well-shielded cavern 627 m downstream of one of the LHC interaction points, the facility will support a broad and ambitious physics program that significantly expands the discovery potential of the HL-LHC. Equipped with four complementary detectors -- FLArE, FASER$ν$2, FASER2, and FORMOSA -- the FPF will enable breakthrough measurements that will advance our understanding of neutrino physics, quantum chromodynamics, and astroparticle physics, and will search for dark matter and other new particles. With this Letter of Intent, we propose the construction of the FPF cavern and the construction, integration, and installation of its experiments. We summarize the physics case, the facility design, the layout and components of the detectors, as well as the envisioned collaboration structure, cost estimate, and implementation timeline.

Astroparticle physics↗
DOE OSTI2024

Barriers to adopting artificial intelligence and machine learning technologies in nuclear power

Artificial intelligence and machine learning (AI/ML) technologies offer unique opportunities to transform nuclear plant operations and power generation. Benefits will be felt not only within existing analog and digital instrumentation and control, but also within work processes, the integration of people with technology and most importantly, the business case. The application of this new technology can help simplify complex problems and produce more effective decision-making, making nuclear power safer, more efficient, and more economically viable in the current energy market. Nonetheless, there are potential barriers to its adoption that must be overcome. The purpose of this paper is to categorize, review, and discuss barriers to AI/ML adoption within the nuclear power industry, with a focus on existing commercial reactors. Unique considerations for advanced reactors are also offered. Here we provide a comprehensive overview of the historical, technical, and business barriers that the industry faces, as well as stakeholder readiness, and end-user acceptance. We underscore the importance of user experience and offer potential solutions in overcoming each barrier. These include provisions for easier plant data access, a friendly regulatory environment, and investment in user trust and explainable AI.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

Large Scale Study of Ligand–Protein Relative Binding Free Energy Calculations: Actionable Predictions from Statistically Robust Protocols

The accurate and reliable prediction of protein–ligand binding affinities can play a central role in the drug discovery process as well as in personalized medicine. Of considerable importance during lead optimization are the alchemical free energy methods that furnish an estimation of relative binding free energies (RBFE) of similar molecules. Recent advances in these methods have increased their speed, accuracy, and precision. This is evident from the increasing number of retrospective as well as prospective studies employing them. However, such methods still have limited applicability in real-world scenarios due to a number of important yet unresolved issues. Here, we report the findings from a large data set comprising over 500 ligand transformations spanning over 300 ligands binding to a diverse set of 14 different protein targets which furnish statistically robust results on the accuracy, precision, and reproducibility of RBFE calculations. We use ensemble-based methods which are the only way to provide reliable uncertainty quantification given that the underlying molecular dynamics is chaotic. These are implemented using TIES (Thermodynamic Integration with Enhanced Sampling). Results achieve chemical accuracy in all cases. Ensemble simulations also furnish information on the statistical distributions of the free energy calculations which exhibit non-normal behavior. We find that the “enhanced sampling” method known as replica exchange with solute tempering degrades RBFE predictions. We also report definitively on numerous associated alchemical factors including the choice of ligand charge method, flexibility in ligand structure, and the size of the alchemical region including the number of atoms involved in transforming one ligand into another. Our findings provide a key set of recommendations that should be adopted for the reliable application of RBFE methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Cinema:Snap: Real-time tools for analysis of dynamic diamond anvil cell experiment data

We report we developed tools and a workflow for real-time analysis of data from dynamic diamond anvil cell experiments performed at user light sources. These tools allow users to determine the phases of matter observed during the compression of materials in order to make decisions during an experiment to improve the quality of experimental results and maximize the use of scarce experimental facility time. The tools fill a gap in dynamic compression data analysis tools that are real-time, are flexible to the needs of high-pressure scientists, connect to automated processing of results, can be easily incorporated into workflows with existing tools and data formats, and support remote experimental data analysis workflows. Specific analytics developed include novel automated two-peak analysis for overlapping peaks and multiple phases, coordinated views of pressure and temperature values, full-compression contour plots, and configurable views of integrated x-ray diffraction. We present an experimental use case to show how the tools produce real-time analytics that help the scientists revise parameters for the next compression

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Analytic results for scalar-mediated Higgs boson production in association with two jets

Abstract We present compact analytic formulae for all one-loop amplitudes representing the production of a Higgs boson in association with two jets, mediated by a colour triplet scalar particle. Many of the integral coefficients present for scalar mediators are identical to the case when a massive fermion circulates in the loop, reflecting a close relationship between the two theories. The calculation is used to study Higgs boson production in association with two jets in a simplified supersymmetry (SUSY) scenario in which the dominant additional contributions arise from loops of top squarks. The results presented here facilitate an indirect search for top squarks in this channel, by a precision measurement of the corresponding cross section. However, we find that the potential for improved discrimination between the Standard Model and SUSY cases suggested by the pattern of results in the one- and two-jet samples is unlikely to be realized due to the loss in statistical power compared to an inclusive analysis.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Relaxation of the degenerate one-dimensional Fermi gas

In this work, we study how a system of one-dimensional spin-1/2 fermions at temperatures well below the Fermi energy approaches thermal equilibrium. The interactions between fermions are assumed to be weak and are accounted for within the perturbation theory. In the absence of an external magnetic field, spin degeneracy strongly affects relaxation of the Fermi gas. For sufficiently short-range interactions, the rate of relaxation scales linearly with temperature. Focusing on the case of the system near equilibrium, we linearize the collision integral and find the exact solution of the resulting relaxation problem. Furthermore, we discuss the application of our results to the evaluation of the transport coefficients of the one-dimensional Fermi gas.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Interleaved Cuk Converter Wave Energy System With Advanced Control and Grid Support Functions for Seamless Integration

This paper presents an innovative wave energy conversion system that integrates an interleaved Cuk converter with advanced nonlinear control for seamless grid integration. The system efficiently extracts power on the DC side using the interleaved Cuk converter, while an inverter manages power transfer to the grid or load on the AC side. A nonlinear control architecture, based on the Lyapunov energy function, ensures stable and optimal operation under varying wave conditions, effectively addressing the challenges of variability and unpredictability inherent in wave energy. The proposed system also incorporates features to enhance power quality and minimize losses, making it a robust solution for renewable energy integration. The system's effectiveness in harnessing wave energy and achieving smooth grid integration is validated through comprehensive computer simulations in MATLAB/Simulink, with case study results demonstrating its capabilities.

HYDRO ENERGY,TIDAL AND WAVE POWER↗
DOE OSTI2023

Towards On-Chip Learning for Low Latency Reasoning with End-to-End Synthesis

The Software Defined Architectures (SODA) Synthesizer is an open-source compiler-based tool able to automatically generate domain-specialized systems targeting Application-Specific Integrated Circuits (ASICs) or Field Programmable Gate Arrays (FPGAs) starting from high-level programming. SODA is composed of a frontend, SODA-OPT, which leverages the multilevel intermediate representation (MLIR) framework to interface with productive programming tools (e.g., machine learning frame-works), identify kernels suitable for acceleration, and perform high-level optimizations, and of a state-of-the-art high-level synthesis backend, Bambu from the PandA framework, to generate custom accelerators. One specific application of the SODA Synthesizer is the generation of accelerators to enable ultra-low latency inference and control on autonomous systems for scientific discovery (e.g., electron microscopes, sensors in particle accelerators, etc.). This paper provides an overview of the flow in the context of the generation of accelerators for edge processing to be integrated in transmission electron microscopy (TEM) devices, focusing on use cases from precision material synthesis. We show the tool in action with an example of design space exploration for inference on reconfigurable devices with a conventional deep neural network model (LeNet). Finally, we discuss the research directions and opportunities enabled by SODA in the area of autonomous control for scientific experimental workflows.

Castellana, Vito G.↗
DOE OSTI2022

Calculation of neutron flux spectra of the VVER-1000 mock-up shielding benchmark with Monte Carlo code MCS utilizing mesh-based weight window

The measurements of neutron spectra compiled inside the NEA-1517/82 package from the Shielding Integral Benchmark Archive and Database (SINBAD) are chosen as benchmark cases to validate the variance reduction technique based on weight window in Monte Carlo Code MCS. A full 3D model for fixed source mode calculation with hexagonal lattice source definition is developed to simulate total of 6 points of measurements at the vicinity of the reactor and the reactor pressure vessel region. A code/code comparison against MCNP6 code is first conducted as verification element for the mesh-based weight window capability in MCS. Finally, the validation results are presented against measurements. The verification against MCNP6 code gives good agreement in addition of the insight to the importance of user understanding to determine proper reference point and reference lower weight bound for scaling which is not required in MCS code due to its capability of automatic scaling. The comparison of neutron spectra between MCS and measurements shows good agreement within 3 standard deviations for all of six detector positions.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2026

Permafrost Thaw, Uneven Subsidence and Projected Drying of Ice-wedge Polygon Tundra: Modeling Archive

This dataset is a model archive of the paper Permafrost Thaw, Uneven Subsidence and Projected Drying of Ice-wedge Polygon Tundra (in prep) to support a modeling study investigating how projected increases in Arctic temperature and precipitation will jointly influence hydrologic conditions in ice-rich tundra landscapes. With this dataset, this study is to address the research question: Will Arctic tundra landscapes become wetter or drier with increasing precipitation and temperature in the future when thaw-induced ground subsidence and associated microtopographic evolution are represented? The simulations focus on ice-wedge polygon tundra, a widespread form of ice-rich permafrost terrain that is highly sensitive to thaw-driven landscape change. This dataset contains model input and output data for four study watersheds in Alaska: Anaktuvuk, Utqiagvik (formerly Barrow), Brooks Foothills, and Prudhoe Bay. Simulations were performed using the Advanced Terrestrial Simulator (ATS, v1.5), a physics-rich integrated surface–subsurface hydrologic model. For each watershed, ten modeling cases were performed representing two landscape evolution conditions (with subsidence and without subsidence) combined with five climate forcing scenarios derived from Shared Socioeconomic Pathways (SSP5, SSP5 with precipitation trend, SSP2, SSP2 with precipitation trend, and SSP2 with double precipitation trend). Particularly, for each watershed under the forcing SSP2 with precipitation trend, there are two additional simulations considering spatially heterogeneous subsidence distributions: one assumes randomly distributed scaling and the other includes elevation dependent distribution scaling. These simulations span 1980–2099 and include spin-up runs (1980–2009) followed by transient projections (2010–2099). To facilitate reproducibility of simulations, all datasets are organized by watershed. For each study watershed, the dataset contains: (1) Pre-partitioned mesh files for 32-core modeling (.par.32.XX), located in EACH_WATERSHED/mesh/basin; and also a non-partitioned mesh file (.exo) located in EACH_WATERSHED/mesh; (2) Climate forcings corresponding to the five SSP scenarios (.h5), located in EACH_WATERSHED/data; (3) Final states (.h5) from column spin-up modeling used to initialize historical watershed-scale spin-up runs from 1980 to 2009, located in EACH_WATERSHED/PreSpinupHistorical; (4) Final states (.h5) of historical watershed-scale spin-up runs from 1980 to 2009 used to initialize projection runs, located in EACH_WATERSHED/Spinup_daymetERA5; (5) ATS modeling input files (.xml), located in EACH_WATERSHED/EACH_SIMULATION_SCENARIO/inputfiles; (6) ATS modeling output files (.dat), located in in EACH_WATERSHED/EACH_SIMULATION_SCENARIO/combined_obs; (7) For the Brooks Foothills watershed, additional spatial model outputs are provided (.h5) for selected years (2033 and 2093) used to generate spatial figures in this study, located in Brooksfoothills/EACH_SIMULATION_SCENARIO/results-WITH/WITHOUT_SUBSIDENCE-year2033/2093. All data files with suffix .h5 can be accessible through Python h5py, and all data files with suffix of .dat can be imported by Python pandas. Mesh file with .exo can be visualized through Paraview or read by Python netCDF. The Next-Generation Ecosystem Experiments in the Arctic (NGEE Arctic) project is a research effort to reduce uncertainty in the Department of Energy’s Energy Exascale Earth System Model (E3SM) by developing a predictive understanding of Arctic tundra ecosystems underlain by permafrost and to quantify feedbacks from the Arctic tundra to the Earth system. NGEE Arctic is supported by the Department of Energy's Office of Biological and Environmental Research. Over Phases 1–3, observations made by the NGEE Arctic team across a gradient of permafrost landscapes in Arctic Alaska improved the representation of tundra processes in the land surface component of E3SM (the E3SM Land Model, ELM). Model improvements emphasized unique aspects of permafrost environments and explored reductions in model complexity while retaining predictive power. The Arctic-informed ELM developed by NGEE Arctic has been used to make novel predictions on processes ranging from permafrost thaw to soil biogeochemical cycling to Earth system feedbacks associated with the unique characteristics of tundra plants. In Phase 4, the NGEE Arctic team is evaluating our new predictive understanding under novel conditions across the Arctic domain. In collaboration with partners at long-term pan-Arctic research sites we are examining whether an Arctic-informed ELM can faithfully simulate interactions among surface and subsurface processes at site, regional, and pan-Arctic scales. In turn, we are using variety of tools to dynamically extend and evaluate ELM inference, with an emphasis on data synthesis and pan-Arctic model evaluation, reintegration of code with an evolving E3SM, scaling across heterogeneous Arctic landscapes, and the appropriate representation of the impacts of increasingly frequent Arctic disturbances.

EARTH SCIENCE > ATMOSPHERE > PRECIPITATION↗
DOE OSTI2020

LANL studies of ESD spark energy discharge through September 2019

Two concentric-sphere apparatuses were used to measure the energies deposited by electric sparks through air to calibrated loads. Both sets of spheres had clean, uninsulated metal surfaces. The 127-mm diameter pair of spheres had a gap of 10 mm and a capacitance of 52 pF. The maximum energy stored on these spheres was 12 mJ and the maximum energy delivered to the 50-mΩ load was 11 µJ, with or without inductance. This load energy amounted to 0.09% of the available input energy; the remainder of the input energy was expended in forming the spark. The second set of spheres was 330 mm in diameter with a gap of 14 mm and a capacitance of 240 pF. The maximum energy stored on these spheres was 71 mJ and the maximum energy delivered to the 50-mΩ load was 150 µJ without added inductance. This load energy was 0.27% of the input energy; again, the remainder of the input energy was expended in forming the spark. The inclusion of 250 nH and 500 nH inductances in the discharge path of the smaller spheres caused the current discharges to resonate, but had little effect on the maximum energies deposited in the loads. At the time of writing, inductances had not yet been added to the larger spheres. The magnitudes of the observed spark discharges were stochastic, so more than 1200 tests were required to develop the statistical bounds of the spark behavior, i.e., to estimate the worst case (highest likely) energy depositions in the loads. The action integrals of the current discharges $∫ i^2dt$ were found to be approximately independent of the load resistances for loads of less than ~1 Ω. Hence the energy deposition scaled with resistance as 207 µJ/Ω and 2.93 mJ/Ω for the two apparatuses.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2020

Interpenetrating Plasma Simulations

This project investigated multifluid models for simulating interpenetrating plasmas. These models solve the Euler equations for each plasma stream along with an appropriate model for electron dynamics. The project developed a novel code, Euclid, that simulates these models using high-order conservative spatial discretization methods and explicit and semi-implicit time integration methods. Euclid was used to solve several multifluid test cases representative of plasma dynamics in high-energy density physics experiments. Kinetic simulations of interpenetrating flows using the LOKI code revealed novel physical effects of the ion-ion streaming instability. A new multi-flow collision operator was developed for the LOKI code. A simple model of the ion-ion streaming instability was also developed. Several presentations were given on the project results; three journal articles have been published, one has been submitted, and two are planned.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Explainable Artificial Intelligence Technology for Predictive Maintenance

The domestic nuclear power plant fleet has relied on labor-intensive and time-consuming preventive maintenance programs, thus driving up operation and maintenance costs to achieve high-capacity factors. Artificial intelligence and machine learning can help simplify complex problems, such as diagnosing equipment degradation, to enable more effective decision-making. Benefits will be felt not only within existing analog and digital instrumentation and control, but also work processes, the integration of people with technology, and most importantly, the business case. Together, these hold promise to make nuclear power more efficient and reduce costs associated with operation and maintenance. While the artificial intelligence and machine learning technologies hold significant promise in the nuclear industry, there are challenges or barriers to their adoption. This report outlines the those different machine learning adoption barriers (categorized as historical, technical, economic, regulatory, and user) that the industry must overcome to realize the full benefits of artificial intelligence and machine learning capabilities for long-term economic sustainability. This report also provides solutions for some of these barriers by focusing on improving the explainability of machine learning to encourage trust from the end-user. Trust and explainability are essential to machine learning adoption. This report focuses on research-developed solutions to some of these barriers while analyzing a non-safety-related system, namely the circulating water system. This system frequently experiences waterbox fouling which our models preemptively diagnoses then explains to the operator how those conclusions were reached. This report presents and discusses the inherent trade-off between machine learning performance (in terms of accuracy) and explainability, where highly accurate machine learning methods (such as deep-learning) are the least explainable, and the most explainable methods (such as decision trees) are the least accurate. In addition, explainability of artificial intelligence techniques in terms of transparency and post-hoc metrics are discussed. This report outlines the importance of data novelty and value of new information in evaluating both the explainability and trustworthiness. Novelty detection helps to establish consistency or inconsistency of the new data with respect to the training data. On the other hand, value of information could be a part of the user-centric visualization recommendation system that request additional information to be collected, thereby strengthening the machine learning outcomes. During this project, a copyrighted user-centric visualization that aligns with a human-in-the-loop approach was developed. The user-centric visualization presents different levels of information and can be tailored as per user credentials to gain user confidence. One of the salient features of the user-centric visualization is it presents machine learning methods with explainability metrics. A simplified version of the user-centric visualization was presented to 32 users with varying levels of machine learning expertise. Feedback was solicited to test the hypothesis that the app contained sufficient explainability and that the users would trust the algorithm. Overall, the app was positively received, and the hypothesis was supported. This report discusses the trust-but-verify framework – a potential approach to build user trust artificial intelligence. The framework discusses trust from the human level to artificial intelligence level. The fundamental premise of the trust but verify framework is derived from an observation of nuclear safety culture (i.e., nuclear power plant personnel do not rely on a singular source of data to make a decision). This also ties back to the user-centric visualization that presents different levels of information to achieve both explainability and trustworthiness of artificial intelligence. Even so, the adoption of artificial intelligence and machine learning in the nuclear industry faces additional barriers, namely regulatory and stakeholder readiness. To overcome these challenges, new solutions must gain regulatory approval and cater to stakeholder needs. The Nuclear Regulatory Committee has a 5-year strategic plan which prepares them for reviewing artificial intelligence technologies in licensee submissions. Early and frequent engagement with the regulator is encouraged. Additionally, artificial intelligence solutions should incorporate human-in-the-loop considerations and offer explainability. Stakeholders must prepare by hiring or training staff to adapt to advancing technology in everyday plant tasks.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Scaling Outlooks on Integrated Energy Systems

The report provides research summaries of two developed theories: data projection to enable multi-scale facility digital interactions and introducing the Evaluation Model Development and Assessment Process (EMDAP) approach to Integrated Energy Systems (IES) design. For the data projection, a two-system scaling case including interactions between thermal storage and hydrogen production is provided. The corresponding facilities are the thermal energy distribution system (TEDS) facility and high temperature steam electrolysis (HTSE) facility at the Dynamic Energy Transport and Integration Laboratory (DETAIL) in Idaho National Laboratory (INL). For the EMDAP adaption to system design, a modified process of the EMDAP was developed and applied to indirect two-tank heat storage system design. System phenomena were identified, ranked, and scaled to discover helpful key relations that would determine the ideal component geometry.

08 HYDROGEN↗
DOE OSTI2025

Coal to Carbon Fiber (C2CF) Continuous Processing for High Value Composites (Final Report)

Coal tar is a condensed and recovered by-product of the coking of metallurgical coal for steel production. The heaviest fraction of distilled coal tar is an isotropic pitch largely used as a binder in the manufacturing of carbonaceous electrodes for primary aluminum smelting and in electric arc furnaces. Coal tar pitch offers high carbon yield upon carbonization. In this project, a process to convert the domestically sourced isotropic coal tar pitch, containing very low particulates (QI = 0.32 wt.%), to form flow-domain mesophase pitch amenable for melt spinning into precursor (green) fibers for carbon fiber, was developed and optimized. The final reproducible processing developed is reviewed in this report, along with several characterizations of the mesophase pitch. A final definition of the characteristics of a ‘spinnable’ mesophase pitch is presented. With this mesophase pitch, reproducible and stable multifilament melt spinning was developed, producing green fiber tows with filament diameters of approximately 20 m. The multifilament melt spinning was the most challenging aspect of the project and required the most effort. The best practices learned from this project for melt spinning are reviewed in this report. Once spun, the green fibers were oxidatively stabilized, carbonized and graphitized under inert gas atmosphere to form the final carbon fibers. Given the relatively high softening point of the mesophase pitch, no issues of interfilament fusion were observed during batch oxidation, and subsequent batch carbonization and graphitization went smoothly in all cases. An ~ 80 wt.% conversion of the green fiber mass to final carbon fiber was achieved. After graphitization, the carbon fibers showed high tensile moduli (most were ~ 600 GPa, or 87 Msi) consistent with commercially-available high-performance pitch-based carbon fiber. However, tensile strength and strain to failure were comparatively low. Further work to reduce defects in and on the fiber surfaces would increase these properties. SEM imaging of the graphitic fiber textures is presented herein. Rudimentary composites were fabricated from the carbon fibers and characterized showing similar modulus to baseline composites fabricated with commercial carbon fiber. Finally, a basic economic analysis was done showing the potential to increase the value of the isotropic coal tar pitch by up to 13.6 to 136 times based on a carbon fiber value of $\$$5/lb to $\$$50/lb, respectively. Moreover, the site case study suggests that the coal tar from the single integrated steel mill could supply production of up to 16 kt/yr of carbon fiber. Finally, a technological gap analysis was done which shed light on remaining technical challenges. These challenges included: recovery and utilization of condensates from the mesophase pitch processing, further advancing and increasing stability of the multifilament melt spinning processing, optimization of the oxidation processing, defect reduction for increased carbon fiber strength, and the development of a weaving process towards carbon fiber fabrics. To maximize the coal value chain, the primary objectives of this project were to (a) develop and scale efficient processing technology for producing melt-spinnable mesophase pitch from isotropic coal tar pitch, (b) clarify and simplify tedious continuous fiber processing technologies (particularly multifilament melt spinning of mesophase pitch) towards the efficient production of high performance carbon fiber, and (c) demonstrate and characterize representative composite parts derived from the final carbon fiber. Immense progress was made on all 3 objectives and is detailed in this report.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2025

Voices from Rural Electric Cooperatives: A Call for a DER Integration Playbook for Rural and Agricultural Income & Savings from Renewable Energy (RAISE)

Rural-serving electric utilities (RSEUs)—including electric cooperatives, municipal systems, and small investor-owned utilities—are essential players in the evolving energy landscape. These community-focused entities are increasingly being asked to consider distributed energy resources (DERs) such as rooftop and ground-mounted solar, wind, battery storage, smart water heaters, and demand response programs (NRECA 2025; Lenhart et al. 2020). Yet the path to DER adoption is far from straightforward in the rural context. This report is based on in-depth interviews with managers of rural electric cooperatives across the United States. These conversations offer a grounded, unvarnished look at how DERs are perceived, what barriers exist, and what conditions might enable integration and adoption. While the utilities interviewed vary in geography, size, and DER experience, several clear and common themes emerged across electric cooperatives such that the report recommends the development of a DER Integration Runbook to help utilities assess readiness, define local use cases, engage stakeholders, pilot projects, and iterate, expanding over time.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
NASA NTRS1972

Generation of the invariant coefficients of the characteristic polynomial for an nxn matrix

In theories of numerical stability, roots to a characteristic polynomial are sought, which, in the case of the predictor with iterative correction method of numerical integration, are eigenvalues of a matrix whose elements depend on the coefficients used in the integration process. The characteristic polynomial is displayed explicitly in terms of the elements of the characteristic matrix.

Beaudet, P. R.↗